Ann Glob Anal Geom (Dordr) 2016 7;50(3):209-235. Epub 2016 Apr 7.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
The aim of this paper is to generalize certain volume comparison theorems (Bishop-Gromov and a recent result of Treude and Grant, Ann Global Anal Geom, 43:233-251, 2013) for smooth Riemannian or Lorentzian manifolds to metrics that are only (differentiable with Lipschitz continuous derivatives). In particular we establish (using approximation methods) a volume monotonicity result for the evolution of a compact subset of a spacelike, acausal, future causally complete (i.e. Read More